Solve the third-order initial value problem below using the method of Laplace transforms y'''-2y"-21y'-18y=-18 y(0)=2 y'(0)=7 y"(0)=95

Khadija Wells 2020-11-09 Answered
Solve the third-order initial value problem below using the method of Laplace transforms
y2y"21y18y=18
y(0)=2
y(0)=7
y"(0)=95
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Expert Answer

Layton
Answered 2020-11-10 Author has 89 answers
Step 1
Taking Laplace Transform in both direction:
L{y2y"21y18y}=L{18}
L{Fn(t)}=snY(s)s2y(0)sy(0)y"(0)
L{y}=s3Y(s)s2y(0)sy(0)y(0)
L{y"}=s2Y(s)sy(0)y(0)
L{y}=sY(s)y(0)
L{y}=Y(s)
[s3Y(s)s2y(0)sy(0)y(0)]2[s2Y(s)sy(0)y(0)]21[sY(s)y(0)]18[Y(s)]=L{18}
[s3Y(s)s2(2)7s95]2[s2Y(s)s(2)7]21[sY(s)2]18[Y(s)]=18s
s32s221s18Y(s)2s27s95+4s+14+42=18s
Y(s)=2s2+3s18s+39s32s221s18=2s3+3s218+39ss(s+1)(s+3)(s6)
Step 2
find the factor:
Y(s)=As+B(s+1)+C(s+3)+D(s6)
Y(s)=2s3+3s218+39ss(s+1)(s+3)(s6)
As+B(s+1)+C(s+3)+D(s6)=2(0)3+3(0)218+39(0)(1)(3)(6)s+2(1)3+3(1)218+39(1)(1)(1+3)(16)(s+1)+2(3)3+3(3)2<
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